Mychal, I know this is an older thread, but I was wondering which movement you converted with, and why your beit din did not approve your alternative patronymic?
I am converting Reform, and although the CCAR issued a responsa against a convert using something other than bat Avraham v' Sarah, a responsa is a guideline recommendation not a ruling, so here's hoping I can use my alternative :)
What's interesting is the Conservative Rabbinical Assembly voted a convert COULD use an alternative.